Question

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Answer 1

Step-by-step explanation:

✬ Sides = 12 , 12 , 18 ✬

✬ Height = 7.94 ✬

Step-by-step explanation:

Given:

• Perimeter of isosceles triangle is 42 cm.
• Length of base of triangle is 3/2 times of equal sides.

To Find:

• Length of each side of triangle and height of triangle.

Solution:

Let ABC be a isosceles triangle where measure of each equal sides be x cm.

AB = AC = x

BC = 3/2 times of x

As we know that

★ Perimeter of ∆ = Sum of all sides ★

A/q

Perimeter (AB + BC + CA) = 42 cm

⟹ 42 = AB + BC + CA

⟹ 42 = x + 3x/2 + x

⟹ 42 = 2x + 3x/2

⟹ 42 = 4x + 3x/2

⟹ 42 × 2 = 7x

⟹ 84/7 = 12 = x

Hence, measure of sides of ∆ABC are ∼

AB = AC = 12 cm

BC = 3/2 × 12 = 18 cm

___________________

[ Now let's find height of the triangle ]

We will use Pythagoras Theorem here.

Let height of triangle be AZ i.e (AZ ⟂ BC, so BZ = ZC)

In right angled ∆AZC we have

• AZ {perpendicular/height}
• ZC {base} = 1/2 × 18 = 9
• AC {hypotenuse} = 12 cm

★ H² = Perpendicular² + Base² ★

➼ AC² = AZ² + ZC²

➼ 12² = AZ² + 9²

➼ 144 – 81 = AZ²

➼ √63 = 7.937 = AZ

Hence, height of the triangle is 7.94 cm.

Answer 2

Answer:

14

Step-by-step explanation:

let the sides of the isosceles triangle be = x

2x + 3/2 = 42

2x = 42•2/3 = 28

x= 28 /2

x= 14

hence the length of the each of triangle is 14

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