Question

1. In triangle ABC ,
AB = AC = x; BC = 10 cm and the area of
the triangle is 60 cm?. Find x.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given,

• Measure of BC = 10 cm
• Area of ∆ABC = 60 cm²
• Measure of AB = AC = x

Here,

$\text{Area of triangle} = \bf \frac{b}{4} \bigg\{ \sqrt{ {4a}^{2} - {b}^{2} } \bigg\} \\ \because \: \text{This triangle has its two} \\ \text{ sides equal and one unequal side.}$

Now,

$= > \frac{10}{4} \bigg \{ \sqrt{ {4x}^{2} - {(10)}^{2} } \bigg\} = 60 \\ \\ = > \sqrt{ {4x}^{2} - {(10)}^{2}} = \frac{60}{ \frac{4}{10} } \\ \\ \\ = > \sqrt{ {4x}^{2} - {(10)}^{2}} = \frac{60 \times 10}{4} \\ \\ = > \sqrt{ {4x}^{2} - {(10)}^{2}} = \frac{600}{4} \\ \\ = > {4x}^{2} - {(10)}^{2} = { \bigg( \frac{600}{4} \bigg)}^{2} \\ \\ = > {4x}^{2} - 100 = \frac{3600}{16} \\ \\ = > \: \: \: \: \: {4x}^{2} = \frac{3600}{16} + 100 \\ \\ = > \: \: \: \: \: \: \: {4x}^{2} = \frac{3600 + 1600}{16} \\ \\ = > \: \: \: \: \: \: {4x}^{2} = \frac{5200}{16} \\ \\ = > \: \: \: \: \: \: \: {x}^{2} = \frac{5200}{16 \times4 } \\ \\ = > \: \: \: \: \: \: \: {x}^{2} = \frac{5200}{64} \\ \\ = > \: \: \: \: \: \: \: {x}^{2} = 81.25 \\ = > \: \: \: \: \: \: \: \: x = \sqrt{81.25} \\ = > \: \: \: \: \: \: \: \: x = 9.0138$

Thus,

• Measure of AB & AC is equal to 9.0138 cm