Question

Diagonal of rectangle is 29cm and breadth is 20cm find its length area and perimeter

Answer 1

Given,

$\pink{ \boxed{\boxed{\begin{array}{cc} \rm \to \: diagonal \: of \: rectangle \: \: d = 29 \: cm \\ \\ \rm \to \: breadth \: of \: rectangle \: \: b = 20 \: cm \\ \\ \underline{ \blue{ \sf \: we \: have \: to \: find \: : }} \\ \\ \rm \to \: area \: of \: \: rectangle \: = A \\ \\ \rm \to \: perimeter \: of \: rectangle \: = S\end{array}}}}$

$\small{\orange{ \boxed{\boxed{\begin{array}{cc} \underline{\downarrow \bf \: formula \: \downarrow} \\ \\ \sf \: we \: know \: that \: for \: recrangle \\ \\ \odot \: \rm \: area \: A = length \times breadth \\ \\ \rm \implies \:A = l \times b \\ \\ \\ \odot \: \rm \: perimeter \: S = 2(length + breadth) \\ \\ \rm \implies \: S =2(l + b) \end{array}}}}}$

At first we have to find length (l)

we know that, for rectangle

$\rm \: diagonal \: \: d = \sqrt{ {l}^{2} + {b}^{2} }$

So,

According to the question,

$29 = \sqrt{ {l}^{2} + {(20)}^{2} } \\ \\ \rm \implies\: {(29)}^{2} = {l}^{2} + 400 \\ \\ \rm \implies\:l = 21 \: cm \\ \\ \rm \: area \: A = 21 \times 20 = 420 \: {cm}^{2} \\ \\ \rm \: perimeter \: S = 2(21 + 20) = 82 \: cm$

Answer 2

The length, area and the perimeter of the rectangle are 21cm, 420 cm² and 82 cm respectively.

Step-by-step explanation:

Let the rectangle be ABCD.

According to the question :

➡➡Diagonal: BD = 29cm

➡➡Breadth : CD = 20cm

45%

All the angles in a rectangle are 90°.

So, ABDC is a right angled triangle with ZBCD = 90°. Using pythagoras theorem:

(P)² + (B)² = (H)²

(BC)² + (20)² = (29)²

➡➡BC² + 400 = 841

BC² = 841 - 400

➡BC² = 441

BC = √441

BC= 21cm

45%

The length of the rectangle BC is 21 cm.

Now, let's find the area of the rectangle :

➡➡➡Area of rectangle = Length

➡➡A = 21cm x 20cm

• ➡➡Area = 420cm²x breadth

.. The area of the rectangle is 420 cm².

Finally, finding the perimeter of the rectangle :

➡➡Perimeter = 2 (1 + b)

P = 2 (21cm + 20cm)

P = 2 (41cm)

➡➡Perimeter = 82cm.

The perimeter of the rectangle is 82 cm.