Question

if a diagonal of a rectangle is 25 cm and its breadth is 7 cm what is perimeter​

Answer 1

$\Large{\underbrace{\sf{\orange{Required\:Solution:}}}}$

Given thαt,

• A diαgonαl of α rectαngle is 25cm.
• And its breαdth is 7cm

◾️We need to find its perimeter.

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To do so, firstly we need to find its length by Pythagoras Theorem.

$\large\star{\boxed{\sf{\orange{ (Base)^{2}+(Perpendicular)^{2} = (Hypotenuse)^{2}}}}}$

• Substitute the values and simplify.

$\longrightarrow{\sf{ (7cm)^{2} + (length)^{2} = (25cm)^{2}}}$

$\longrightarrow{\sf{ 49cm^{2} + (length)^{2} = 625cm^{2}}}$

$\longrightarrow{\sf{ (length)^{2} = 625cm^{2} - 49cm^{2}}}$

$\longrightarrow{\sf{ (length)^{2} = 576cm^{2}}}$

$\longrightarrow{\sf{ length = \sqrt{576cm^{2}}}}$

$\longrightarrow{\sf{ length = 24cm}}$

$\large\star{\boxed{\sf{\orange{ Perimeter_{(rectangle)} = 2(length+breadth)}}}}$

• Substitute the values and simplify.

$\longrightarrow{\sf{2(24+7)}}$

$\longrightarrow{\sf{2\times 31}}$

$\large{:}\implies{\boxed{\sf{\orange{ 62cm}}}}$

Therefore, the perimeter of the rectangle is 62m.

And we are done! :D

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