Download App

Perimeter and Areas of Plane Figures — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsPerimeter and Areas of Plane Figures5 Marks
Question
The difference between the sides at right angle in a right-angled triangle is 7cm. The area of the triangle is $60cm^2.$ Find its perimeter.
✓

Answer

Given:
Area of triangle $= 24cm^2$​​​​​​​
Let the sides be a and b, where a is the height and b is the base of triangle.
a - b = 2cm a - b = 2cm
a = 2 + b ...(1)
Area of triangle $=\frac{1}{2}\times\text{b}\times\text{h}$
$\Rightarrow24=\frac12\times\text{b}\times(2+\text{b})$
$\Rightarrow48=\text{b}+\frac12\text{b}^2$
$\Rightarrow48=2\text{b}+\text{b}^2$
$\Rightarrow\text{b}^2+2\text{b}-48=0$
$\Rightarrow(\text{b}+8)(\text{b}-6)=0$
$\Rightarrow\text{b}=-8$ or 6
Side of a triangle cannot be negative.
Threfore, b = 6cm.
Substituting the value of b = 6cm, in equatin (1) we get:
a = 2 + 6 = 8cm
Now, a = 8cm, b = 6cm
Now, in the given right triangle, we have to find third side.
Using the relation
$(Hyp)^2 = (Oneside)^2 + (Otherside)^2$
$\Rightarrow Hyp^2 = 8^2 + 6^2$
$\Rightarrow Hyp^2 = 64 + 36$
$\Rightarrow Hyp^2 = 100$
$\Rightarrow Hyp = 10cm$
So, the third side is 10cm.
So, Perimeter of a triangle = a + b + c.
$\therefore$ required perimeter of the triangle = 8 + 6 + 10 = 24cm.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Perimeter and Areas of Plane Figures→Perimeter and Areas of Plane Figures — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Prove that the square of any positive integer is of the form 4q or 4q + 1 for some integer q.
→
Solve the following quadratic equations by factorization:
$\text{x}^2-\big(\sqrt{2}+1\big)\text{x}+\sqrt{2}=0$
→
If $\text{x}=\text{a}\sec\theta+\text{b}\tan\theta$ and $\text{y}=\text{a}\tan\theta-\text{b}\sec\theta,$ prove that $\big(\text{x}^2+\text{y}^2\big)=\big(\text{a}^2-\text{b}^2\big).$
→
Solve the following systems of equations by using the method of cross multiplication:
$2x + y = 35,$
$3x + 4y = 65$
→
Draw the less than type ogive for this data and use it to find the median weight.
→
A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find the length and breadth of the park.
→
Draw a right triangle in which the sides (other than the hypotenuse) arc of lengths 4cm and 3cm. Now, construct another triangle whose sides are $\frac{5}{3}$ times the corresponding sides of the given triangle.
→

Form the pair of linear equations in the problem, and find it's solution graphically.
10 students of class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

→
Find the distance between of the following points from the origin:
B(-5, 5)
→
The following table gives the frequency distribution of married women by age at marriage:
Age (in years)
Frequency
15-19
53
20-24
140
25-29
98
30-34
32
35-39
12
40-44
9
45-49
5
50-54
3
55-59
3
60 and above
2
Calculate the median and interpret the results.
→