Question

if a diagnol of a rectangle is 53 cm nd one side is 28 cm , find the other side.
A) 25 cm
B) 45 cm
C) 45 sq. cm​

Answer 1

Correct Question

If a diagonal of a rectangle is 53 cm and one side is 28 cm, find the other side.

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Given

The Diagonal of Rectangle = 53 cm

One Side = 28 cm

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To Find

The other side.

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Solution

We will use the Pythagorean Theorem in this question.

Pythagorean Theorem ⇒ Base² + Height² = Hypotenuse²

Base ⇒ x cm

Height ⇒ 28 cm

Hypotenuse ⇒ 53 cm

So we will solve this equation to find the Base ⇒ x² + (28)² = (53)²

Let's solve your equation step-by-step.

x² + (28)² = (53)²

Step 1: Simplify the equation.

⇒ x² + (28)² = (53)²

⇒ x² + 784 = 2809

Step 2: Subtract 784 from both sides of the equation.

⇒ x² + 784 - 784 = 2809 - 784

⇒ x² = 2025

Step 3: Find the square root of 2025.

⇒ √x = √2025

$\begin{array}{r | l} 3 & 2025 \\ \cline{2-2} 3&675 \\ \cline{2-2} 3 &225 \\ \cline{2-2} 3& 75 \\ \cline{2-2}5 & 25\\ \cline{2-2} & 5\\ \end{array}$

2025 = 3×3×3×3×5×5

2025 = (3×3) × (3×3) × (5×5)

√2025 = 3 × 3 × 5

√2025 = 45

⇒ x = 45

∴ The other side is (b) 45 cm.

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Answer 2

Answer:

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\sf\large{A}}\put(9.6,1.7){\sf53 cm}\put(7.7,1){\sf\large{B}}\put(9.2,0.7){\sf?}\put(11.1,1){\sf\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,2){\sf28 cm}\put(8,1){\line(3,2){3}}\put(11.1,3){\sf\large{D}}\put(10.8,1){\line(0,2){0.2}}\put(10.8,1.2){\line(2,0){0.2}}\end{picture}$

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We know that Diagonal of Rectangle divides it into two Equal Right Angle Triangle. Hence, we will use Pythagoras Theorem to find another side of Triangle.

$\underline{\bigstar\:\textsf{By Pythagoras Theorem in \triangle BCD :}}$

$:\implies\sf (Hypotenuse)^2=(Base)^2+(Height)^2\\\\\\:\implies\sf (BD)^2=(BC)^2+(CD)^2\\\\\\:\implies\sf (53)^2=(BC)^2+(28)^2\\\\\\:\implies\sf (53)^2-(28)^2=(BC)^2\\\\{\scriptsize\qquad\bf{\dag}\:\:\frak{(a^2-b^2)=(a+b)(a-b)}}\\\\:\implies\sf (53 + 28)(53 - 28) =(BC)^2\\\\\\:\implies\sf 81 \times 25=(BC)^2\\\\\\:\implies\sf \sqrt{81 \times 25} = BC\\\\\\:\implies\sf \sqrt{9 \times 9 \times 5 \times 5} = BC\\\\\\:\implies\sf 9 \times 5 = BC\\\\\\:\implies\underline{\boxed{\sf BC = 45 \:cm}}$

⠀

$\therefore\:\underline{\textsf{Other side of the rectangle is B) \textbf{45 cm}}}.$