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Standard VIII

Mathematics

Construction of Isosceles Triangle Whose Base and Corresponding Altitude Are Given

Construct ABC...

Question

Construct $∆$ ABC, in which BC =5.2 cm, $∠$ ACB = $45^{°}$ and perimeter of $∆$ ABC is 10 cm.

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Solution

Perimeter of △ABC = 10 cm
⇒ AB + BC + AC = 10 cm
⇒ AB + 5.2 + AC = 10 cm
⇒ AB + AC = 4.8 cm
A triangle can be only possible if the sum of the sides of a traingle is greater than the third side.
But here, AB + AC < BC
Hence, the construction of △ABC is not possible.

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Similar questions

Q. Write the steps to construct

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∠ A C B = 45^{\circ}

and perimeter of

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Q. Construct

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Q. Construct a ∆ABC in which AB = AC = 5.2 cm and ∠A = 120°. Draw AD ⊥ BC.

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Construct ∆ ABC, in which BC =5.2 cm, ∠ACB = 45° and perimeter of ∆ ABC is 10 cm.

Perimeter of △ABC = 10 cm ⇒ AB + BC + AC = 10 cm ⇒ AB + 5.2 + AC = 10 cm ⇒ AB + AC = 4.8 cm A triangle can be only possible if the sum of the sides of a traingle is greater than the third side. But here, AB + AC < BC Hence, the construction of △ABC is not possible.

Construct $∆$ ABC, in which BC =5.2 cm, $∠$ ACB = $45^{°}$ and perimeter of $∆$ ABC is 10 cm.

Perimeter of △ABC = 10 cm
⇒ AB + BC + AC = 10 cm
⇒ AB + 5.2 + AC = 10 cm
⇒ AB + AC = 4.8 cm
A triangle can be only possible if the sum of the sides of a traingle is greater than the third side.
But here, AB + AC < BC
Hence, the construction of △ABC is not possible.