Question

18. If the length of a diagonal of a rectangle of length 16 cm is 20 cm, then its area is
(a) 192 cm²
(b) 320 cm²
(c) 160 cm²
(d) 156 cm²​

Answer 1

Step-by-step explanation:

192 is answer

Length l of rectangle = 16cm

Diagonal D of rectangle = 20cm

We have to find breadth of rectangle.

Let the breadth be b.

(diagonal)² = length² + breadth ²

(20)² = (16)² +(b)²

400=256+b²

b² = 400-256

b² = 144

b= √144

b= 12

Breadth b of rectangle = 12cm

Area of rectangle = length × breadth

= 16 × 12

= 192cm²

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Answer 2

✫ ANSWER ✫

(a) 192 cm² (✔)

GIVEN:

• Diagonal of a rectangle(AC) = 20 cm
• Length of the rectangle(AB) = 16 cm

TO FIND:

• What is the area of the rectangle ?

SOLUTION:

Firstly, we have to find the base (BC) of the rectangle

✎ To find the base of the rectangle, we use the Pythagoras theorem

$\bf{\star \: (Hypotenuse)^2 = (base)^2 + (Perpendicular)^2 \: \star}$

• Hypotenuse = 20 cm
• Base = 'b' cm
• Perpendicular = 16 cm

On putting the given values in the formula, we get

$\rm{\dashrightarrow (20)^2 = (b)^2 + (16)^2}$

$\rm{\dashrightarrow 400 = b^2 + 256 }$

$\rm{\dashrightarrow 400 - 256 = b^2}$

$\rm{\dashrightarrow 144 = b^2 }$

$\rm{\dashrightarrow \sqrt{144} = b }$

$\bf{\dashrightarrow \star \: 12 \: cm = b \: \star}$

❛ The base of the rectangle is 12 cm ❜

We know that the formula for finding the area of rectangle is:-

$\large\bf{\star \: Area = Length \times Breadth \: \star}$

• Length = 16 cm
• Breadth = 12 cm

According to question:-

$\rm{\dashrightarrow Area = 16 \times 12 }$

$\bf{\dashrightarrow \star \: Area = 192 \: cm^2 \: \star}$

❝ Hence, the area of rectangle is 192 cm² ❞

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