Question

the breadth of a rectangle is 5cm and each of its diagonal measures 13cm . find its length

answer:12 cm.

I need this answer with step by step explanation.....​

Answer 1

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

Given thαt,

• The breαdth of α rectαngle is 5cm.
• Eαch of its diαgonαl meαsures 13cm.

◾️We need to find its length.

_________

To do so,

We'll use Pythagoras Theorem.

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

• Substitute the values and simplify.

$\longrightarrow{\sf{ (CD)^{2} + (AC)^{2} = (AD)^{2}}}$

$\longrightarrow{\sf{ (length)^{2} + (5)^{2} = (13)^{2}}}$

$\longrightarrow{\sf{ (length)^{2} + 25= 169}}$

$\longrightarrow{\sf{ (length)^{2}= 169-25}}$

$\longrightarrow{\sf{ (length)^{2}= 144}}$

$\longrightarrow{\sf{ length= \sqrt{144}}}$

$\large\implies{\boxed{\sf{\red{ length= 12}}}}$

Hence, the length is 12cm.

And we are done! :D

__________________________

Answer 2

Answer:

Explanation:

Given :

• breadth of a rectangle is 5 cm.
• it's diagonal measures 13 cm.

To Find :

• It's length.

Formula to be used :

• Pythagoras theorem, ie,, (Diagonal)² = (Breadth)² + (Length)².
• (a)² - (b)² = (a + b) (a - b)

Solution :

★Length,

(Diagonal)² = (Breadth)² + (Length)²

→ (13)² = (5)² + (Length)²

→ (Length)² = (13)² - (5)²

→ (Length)² = (13 + 5) × (13 - 5)

→ (Length)² = 18 × 8

→ (Length)² = 144

→ Length = √144

→ Length = 12 cm

Hence, Length is equal to 12 cm.