Name: The Area Around the Edges
Uploaded: 2019-07-19
Duration: 4 min 16 s
Description: The area enclosed between two figures drawn one inside the other is the area around the edges. Learn how to calculate the area around the edges of a given sh...

Question

The difference between the sides at the right angles in a right-angled triangle is

7 cm

. The area of the triangle is

60 {cm}^{2}

. Find its perimeter.

Accepted Answer

Consider the given data.
The area of the triangle $(A)$ is $60 {cm}^{2}$ .
Let the sides of the triangle be $a$ , $b$ and $c$ .
Where, $a$ is the height, $b$ is the base and $c$ is hypotenuse of the triangle.
Therefore,
$a - b = 7 cm$
Rearrange the equation.
$a = 7 + b . . . . . . (1)$
Write the formula for the area of triangle $(A)$ .
$A = \frac{1}{2} b h . . . . . . (2)$
Substitute $(7 + b)$ for $h$ and $60 {cm}^{2}$ for $A$ in Equation (2).
$60 {cm}^{2}$
Here, the side of a triangle cannot be negative. Therefore, $b = 8 cm$ .

Substituting $8 cm$ for $b$ in Equation ( $1$ ).
$a = 7 + 8 \Rightarrow a = 15 cm$
Now, in the given right triangle, we have to find third side.
$c^{2} = a^{2} + b^{2} \Rightarrow c = \sqrt{a^{2} + b^{2}} . . . . . . (3)$
Substituting $a = 15 cm$ and $b = 8 cm$ in Equation (3).
$c = \sqrt{{(15)}^{2} + {(8)}^{2}} \Rightarrow c = \sqrt{225 + 64} \Rightarrow c = \sqrt{289} \Rightarrow c = 17 cm$
Therefore, the third side is $17 cm$ .

Write the formula for the perimeter of a triangle $(P)$ .
$P = a + b + c$
Substitute the required values in the equation and find the perimeter of a triangle.
$P = 15 + 8 + 17 \Rightarrow P = 40 cm$
Therefore, the perimeter of the triangle is $40 cm$ .

The difference between the sides at the right angles in a right-angled triangle is $7 cm$ . The area of the triangle is $60 {cm}^{2}$ . Find its perimeter.

Important Questions on Perimeter and Area of Plane Figures

Learn and Prepare for any exam you want !

The difference between the sides at the right angles in a right-angled triangle is 7 cm. The area of the triangle is 60 cm2. Find its perimeter.

Important Questions on Perimeter and Area of Plane Figures

Learn and Prepare for any exam you want !

The difference between the sides at the right angles in a right-angled triangle is $7 cm$ . The area of the triangle is $60 {cm}^{2}$ . Find its perimeter.