Herons Formula Test

Result

Herons Formula Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

If the area of an isosceles right triangle is 8 cm², what is the perimeter of the triangle?

A
8 + √2 cm

B
8 + 4√2 cm

C
4 + 8√2 cm

D
12√2 cm

Solution

We know that, area of a right-angle triangle = ½ × base × height

Now, for an isosceles right-angled triangle, base = height

Therefore,

Let base = height = x

Area = ½ × x × x = 8

x² = 16

x = 4 cm

Now, hypotenuse will be given by,

(Hypotenuse)² = 4² + 4²

Hypotenuse = 4√2 cm
Perimeter = 4 + 4 + 4√2

= 8 + 4√2 cm

Hence, B is the correct answer.
Question 2
1 / -0

The lengths of ΔABC are consecutive integers. If ΔABC has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC?

A
4

B
6

C
8

D
10

Solution

Side of equilateral triangle = 9 cm

The perimeter of equilateral triangle = 3 × 9 cm

= 27 cm

Let the lengths of ΔABC be (x – 1), x, and (x + 1).

Perimeter of triangle = 27

x – 1 + x + x + 1 = 27

3x = 27

x = 9 cm

Length of shortest side = x – 1 = 9 – 1 = 8 cm

Hence, C is the correct answer.