Question

the perimeter of the triangle of an isosceles triangle is 42 cm and its base is (3\2) times each equal sides .find the length of each side of the triangle are of the triangle and height of the triangle?pls give me ans

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Answer 1

✬ 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

$\implies{\rm }$ 42 = AB + BC + CA

$\implies{\rm }$ 42 = x + 3x/2 + x

$\implies{\rm }$ 42 = 2x + 3x/2

$\implies{\rm }$ 42 = 4x + 3x/2

$\implies{\rm }$ 42 × 2 = 7x

$\implies{\rm }$ 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

$Let \: equal \: sides \: be \: x</p><p>unequal \: side = 3x/2</p><p></p><p>now \: given</p><p>\begin{gathered}x + x + \frac{3x}{2} = 42 \\ = > \frac{2x}{2} + \frac{2x}{2} + \frac{ 3x}{2} = 42 \\ = > \frac{7x}{2} = 42 \\ x = 42 \times \frac{2}{7} \\ x = 12\end{gathered}x+x+23x=42=>22x+22x+23x=42=>27x=42x=42×72x=12</p><p>Now \: equal \: sides \: are 12</p><p>so \: unequal \: side = 3/2 × 12</p><p>=> 3 × 6</p><p>= 18</p><p></p><p></p><p></p><p>For \: finding \: Height \: drop \: a \: perpendicular. \: </p><p>The \: perpendicular \: will \: cut \: the \: base \: 18 cm \: into \: half \: that \: is \: 9cm</p><p></p><p>Now \: by \: Pythagoras \: theorem</p><p></p><p>Height² + 9² = 12² (since 12 becomes \: hypotenuse \: of \: the \: triangle \: formed \: by \: perpendicular)</p><p></p><p>height² = 12² - 9²</p><p>height ² = 144 - 81</p><p>height² = 63</p><p>height = √63</p><p>height = 7.93</p><p>$