Triangle has sides

MATHEMATICS · Multi-part · CBSE · Mathematics · Heron's Formula · Heron's Formula

Problem

Triangle

PQR

has sides

12\,\text{cm}

15\,\text{cm}

and

17\,\text{cm}

. Triangle

ABC

is formed by adding

2\,\text{cm}

to the shortest side and subtracting

2\,\text{cm}

from the longest side of

PQR

, leaving the remaining side unchanged. Hence the sides of

\triangle ABC

are

14\,\text{cm}

15\,\text{cm}

and

15\,\text{cm}

. Both triangles therefore have the same perimeter. (i) Calculate the area of

\triangle PQR

. (ii) Calculate the area of

\triangle ABC

. (iii) State which triangle has the larger area and by how much. (iv) Comment briefly on how redistributing the side lengths while keeping the perimeter fixed affected the area.

Related theory

Heron's Formula
Area of Triangles
Triangle area and perimeter
Mensuration

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