Download App

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

Gujarat BoardEnglish MediumSTD 10MathsPerimeter and Area of Plane Figures4 Marks
Question
The difference between the sides at right angle in a right-angled triangle is $7\ cm$. 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
$(\text { Hyp })^2=(\text { Oneside })^2+\text { (Otherside }^2 $
$\Rightarrow \text { Hyp }^2=8^2+6^2 $
$\Rightarrow \text { Hyp }^2=64+36 $
$\Rightarrow \text { Hyp }^2=100$
$\Rightarrow \text { Hyp }=10 \mathrm{~cm}$
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 "4 Marks Questions" from Perimeter and Area of Plane Figures→Perimeter and Area of Plane Figures — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Find the number of term of the $AP -12, -9, -6, ....,21$. If i is added to each term of this $AP$ then find the sum of all terms of the $AP$ thus obtained.
→
Two opposite vertices of a square are $(-1, 2)$ and $(3, 2)$. Find the coordinates of other two vertices.
→
Find the roots of the following equations, if they exist, by applying the quadratic formula:
$\frac{\text{m}}{\text{n}}\text{x}^2+\frac{\text{n}}{\text{m}}=1-2\text{x}$
→
If $18, a,(b-3)$ are in AP, then find the value of $(2 a-b)$.
→
Show graphically that the following systems of equations is in-consistent (i.e. has no solution):
$3\text{x}-4\text{y}-1=0$
$2\text{x}-\frac{8}{3}\text{y}+5=0$
→
Solve for $x$ and $y$
$\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=2,$
$\text{ax}-\text{by}=\text{a}^2-\text{b}^2$
→
A two-digit number is such that the product of the digits is $16$. When $54$ is subtracted from the number, the digits are interchanged. Find the number.
→
The sum of two natural numbers is $28$ and their product is $192$. Find the numbers.
→
The perimeter of a rectangular field is $82\ m$ and its area is $400m^2$. Find the breadth of the rectangle.
→
Solve the following quadratic equations by factorization:
$ a^2 x^2-3 a b x+2 b^2=0 $
→