Question

the diognal of a rectange is 34 cm and breadth is 16 cm. find length and area​

Answer 1

Answer: Hi ,

Diagonal of a rectangle ( d ) = 34 cm

Breadth ( b ) = 16 cm

Let the length = l cm

l² = d² - b²

= ( 34 )² - ( 16 )²

= ( 34 + 16 ) ( 34 - 16 )

= 50 × 18

= 900

l = √ 900

l = 30 cm

Area of the rectangle = lb

A = 30 × 16

A = 480 sq cm

I hope this helps you.

:)

Step-by-step explanation:

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

The diagonal of a rectangle is 34 cm & breadth is 16 cm.

$\underline{\bf{Explanation\::}}$

Let the length of a rectangle be r

As we know that formula of the diagonal of the rectangle;

$\boxed{\bf{Diagonal\:(D) = \sqrt{(L)^{2} + (B)^{2}}}}$

A/q

$\longrightarrow\tt{(D)^{2} = (L)^{2} + (B)^{2}}$

$\longrightarrow\tt{(34)^{2} = (r)^{2} + (16)^{2}}$

$\longrightarrow\tt{1156 = (r)^{2} + 256}$

$\longrightarrow\tt{ (r)^{2} = 1156 - 256}$

$\longrightarrow\tt{ (r)^{2} = 900}$

$\longrightarrow\tt{ r= \sqrt{900} }$

$\longrightarrow\bf{ r= 30\:cm}$

∴ The length of a rectangle will 30 cm .

Now,

As we know that formula of the area of rectangle;

$\boxed{\bf{Area = Length \times breadth \:\:\:(sq.unit) }}$

→ Area = Length × Breadth

→ Area = 30 cm × 16 cm

→ Area = 480 cm²

Thus,

The area of the rectangle will be 480 cm² .