Question

If the diagonal of a rectangle is 41cm and breadth of the rectangle is 9cm ,find the length of the rectangle
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Answer 1

Answer:

ans

Step-by-step explanation:

Diagonal of rectangle = 41cm

Breadth of rectangle = 9cm

length of rectangle = l

rectangle forms 90° angle so when diagonal is drawn then it form right angled triangle

so here ,

diagonal = hypotenuse = 41cm

height = breadth = 9cm

base = length = l

(hypotenuse)² = (height)² + (base)²

(41)² = (9)² + (l)²

1681 = 81 + l²

1681 - 81 = l²

1600 = l²

✓1600 = l

40 = l

therefore length of rectangle is 40cm.

hope this helps u

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Answer 2

Question

If the diagonal of a rectangle is 41cm and breadth of the rectangle is 9cm ,find the length of the rectangle.

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Required Answer

• 40cm

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Given-

• diagonal=41cm
• breadth=9cm

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

To Find-

• length of rectangle=?

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Formula Using-

${\large{\underline{\pmb{\frak{Formula\:for\:hypotenuse}}}}}$

$\bigstar{\underline{\boxed{\red{\sf{H^2=B^2+He^2}}}}}$

Here-

• H=Hypotenuse
• B=Base
• He=Height

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\qquad{\qquad{\qquad{\Large{\underline{\underline{\blue{\sf{Solution}}}}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\large{\underline{\pmb{\frak{Calculating\:Breadth}}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{H^2=B^2+He^2}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{(41)^2=B^2+(9)^2}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{1681=B^2+81}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{B^2=1681-81}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{B^2=1600}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{B=\sqrt{1600}}}}}$

${\pink{\rightsquigarrow}{\qquad{\underline{\red{\sf{length=40}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

Note-B here is referred as length according to formula of hypotenuse.

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

~Therefore

• length of rectangle is 40cm

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$