Question

Question:

If the length and diagonal of a rectangle are 143m and 145m,find its area.

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Answer with whole method​

Answer 1

Before, finding the answer. Let's find out on how we can find the answer.

• To find the Breadth, We must use the formula of Pythagorean Theorem which is  :

$\boxed{ \sf Pythagorean \: Theorem= \sqrt{ a^{2} + b^{2}} }$

• Then, we must find the Area of Rectangle by using the formula of :

$\boxed{ \sf Area \: of \: Rectangle = l \times b }$

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Given :

• Length = 143 m
• Diagonal = 145 m

To find :

• Area of Rectangle

Solution :

Diagonal of rectangle by Pythagorean Theorem = √a² + √b²

145 = √(143)² + √b²

• Squaring both the sides,

145² = 143² + b²

145² - 143² = b²

(145 - 143)(145 + 143) = b²

(2)(288) = b²

576 = b²

B = 24 m

• Now, we know that Breadth = 24 m.

So, Area of rectangle = l × b

= 143 × 24

= 3432 m²

Hence, Area of Rectangle is 3432 m².

Answer 2

Given:

• Length of a rectangle is 142 m.
• Diagonal of the rectangle is 145 m.

To find:

• The area of the rectangle.

Formulae used:

• Pythagorean Theorem: (Perpendicular)² + (Base)² = (Hypotenuse)²
• Area of rectangle = (Length × Breadth) sq.units

Solution:

As we're asked to find the area of the rectangle, we need the measure of its breadth. How can we find it?

Look at the attachment! You can view the diagram of a rectangle OKAY with length 142 m and a diagonal 145 m. Now, scrutinize the view of the diagonal along with with length and breadth. You can notice a right-angled triangle KAY, where:

• KY = Diagonal = Hypotenuse = 145 m
• YA = Length = Base = 142 m
• KA = Breadth = Perpendicular = ?

Now, we can find the perpendicular, i.e, the breadth of the rectangle by using Pythagorean Theorem.

$\underline{ \boxed{ \sf{ \pmb{{Perpendicular\: }^{2} + {Base \: }^{2} = {Hypotenuse \: }^{2} }}}}$

On substituting the measures:-

$\longmapsto{ \sf{ {(KA)}^{2} + {(YA)}^{2} = {(KY)}^{2} }} \\ \\ \longmapsto{ \sf{ {(KA)}^{2} + {(142)}^{2} = {(145)}^{2} }} \\ \\ \longmapsto{ \sf{ {(KA)}^{2} + 20164 = 21025 }} \\ \\ \longmapsto{ \sf{ {(KA)}^{2} = 21025 - 20164 }} \\ \\ \longmapsto{ \sf{ {(KA)}^{2} = 861}} \\ \\ \longmapsto{ \sf{KA = \sqrt{861} }} \\ \\ \longmapsto { \underline{ \underline{ \sf{ \pmb{KA = 29.3}}}}}$

Since the measure of base perpendicular equals the measure of breadth, the breadth of the rectangle is 29.3 m

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Now we shall find the area of the rectangle!

• Length = 143 m
• Breadth = 29.3 m

On substituting these measures in the formula:

$\underline{ \boxed{ \sf{ \pmb{Area_{(rectangle)} =( Length \times Breadth) \: sq.units}}}}$

$\longmapsto{ \sf{Area_{(rectangle)} = 143 \times 29.3}} \\ \\ \longmapsto {\underline{\underline{ \tt{ \pmb{ \red{Area_{(rectangle)} = 4189.9 \: {m}^{2} }}}}}}$

$\\ \\ \therefore \underline{ \frak{ \pmb{The \: area \: of \: the \: rectangle \: is \gray{\: \: 4189.9 \: {m}^{2} }}}}$

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