Question

if each side of a rhombus is 13 cm and the length of one diagonal is 24 cm find the length of other diagonal​

Answer 1

Given :-

• Each side of a rhombus is 13 cm and the length of one diagonal is 24 cm

To find :-

• Length of other diagonal

Solution :-

Let

• AC = 24 cm
• AB = BC = CD = DA = 13 cm

As we know that

• Adjacent sides of rhombus are equal
• Diagonals of rhombus bisect each other at 90°

→ AC = ½ OC = 24

→ OC = 12 cm

By Pythagoras theorem

→ (hypotenuse)² = (base)² + (perpendicular)²

→ (h)² = (b)² + (p)²

→ (DC)² = (OD)² + (OC)²

→ (13)² = (OD)² + (12)²

→ 169 = OD² + 144

→ OD² = 169 - 144

→ OD² = 25

→ OD = √25

→ OD = 5 cm

• BD = 2OD
• BD = 2 × 5 = 10cm

Hence,

• Length of other diagonal of rhombus is 10cm

More to know :-

• Area of circle = πr²
• Circumference of circle = 2πr
• Perimeter of rectangle =2(l + b)
• Perimeter of square = 4 × side
• Area of square = side × side
• Area of rhombus = ½ × product of diagonals
• Area of Parallelogram = base × height
• Area of trapezium = ½ × sum of parallel sides × height

Answer 2

Answer:

120cm²

Step-by-step explanation:

so first we should divide the diagonal

now a triangle ABC

the angle is 90degree

now by Pythagoras theorem

(AC)²=(AB)²+(CA)²

now we have AC as 13cm

n AC=12

so it is

(13)²=(12)²+(CA)²

169=144+(CA)²

(CA)²=169-144

(CA)²=25

CA=5

so another diagonal =CA×2

=5×2

=10

so Area =½×10×24

=120cm²