A survey team measures a rectangular plot of land. The length of the plot is 35 m and the diagonal connecting two opposite corners is 37 m. Find the width of the plot.
12 m
In a rectangle, the length, width, and diagonal form a right triangle, so by the Pythagorean theorem: \(\text{diagonal}^2 = \text{length}^2 + \text{width}^2\).
Substituting the given values: \(37^2 = 35^2 + w^2 \Rightarrow 1369 = 1225 + w^2\).
So \(w^2 = 144\), giving \(w = 12\).
The width of the plot is 12 m.
Important Questions from Quadrilaterals
What is the value of AC 2– BD 2
What is the point of intersection of the diagonals?
What is the area of the parallelogram?
ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD = 35°, then what is the measure of ∠BAC?
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC CD and DA at P, Q, R and S, respectively. If AS = 6 cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:
