Question

1. The length of a rectangle is 12 m and the length of its diagonal is 15 m. Find the
area of the rectangle.​

Answer 1

Answer:

• 108 m² is the required Area.

Step-by-step explanation:

• Length of rectangle ,l = 12 m

• Diagonal ,d = 15 m

Firstly we calculate the breadth of the rectangle .

Using Pythagoras Theorem

• h² = p² + b²

→ AC² = AB² + BC²

→ 15² = 12² + BC²

→ 225 = 144 + BC²

→ BC² = 225-144

→ BC² = 81

→ BC =√81

→ BC = 9m

Now, Calculating the area of rectangle

• Area of Rectangle = Length× Breadth

→ Area = l×b

Substitute the value we get

→ Area = 12×9

→ Area = 108 m²

• Hence, the required Area is 108m².

Answer 2

Answer:

Given :-

• Length of rectangle = 12 m
• Diagonal of rectangle = 15 m

To Find :-

Area of rectangle

SoluTion :-

Here we will use Pythagoras theorem

$\huge \tt \: {h}^{2} = {p}^{2} + {b}^{2}$

P denotes Perpendicular

B denotes Base

H denotes Hypotenuse

Here,

Diagonal -: Hypotenuse

Length -: Perpendicular

Breadth -: Base

$\tt \: {15}^{2} = {12 }^{2} + {b}^{2}$

$\tt \: 225 = 144 + {b}^{2}$

$\tt \: {b}^{2} = 255 - 144$

$\tt \: {b}^{2} = 81$

$\tt \: b = \sqrt{81}$

$\tt \: b = 9$

Now,

As we know that Area = length × Breadth

$\tt \: Area \: = 12 \times 9$

$\tt \: Area \: = 108 \: sq. \: cm$