Q1
A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the wall is:
📝 SolutionBy Pythagoras theorem: $\text{base}^2 = 10^2 - 8^2 = 100 - 64 = 36$, so base $= 6$ m.
Q2
Assertion (A): In $\triangle ABC$, if $DE \parallel BC$ and $\frac{AD}{DB} = \frac{3}{5}$, then $\frac{AE}{EC} = \frac{3}{5}$.
Reason (R): A line parallel to one side of a triangle divides the other two sides proportionally.
Choose the correct option:
Reason (R): A line parallel to one side of a triangle divides the other two sides proportionally.
Choose the correct option:
📝 SolutionBy the Basic Proportionality Theorem, $DE \parallel BC$ implies $\frac{AD}{DB} = \frac{AE}{EC}$, so A is true, and R is exactly the theorem that explains it.
Q3
In two similar triangles, if one triangle's side is 3 times the corresponding side of the other, the ratio of their areas is:
📝 SolutionRatio of areas $= (\text{ratio of sides})^2 = 3^2 : 1^2 = 9:1$.
Q4
Which of the following is sufficient to prove two right triangles similar?
📝 SolutionBoth triangles already share the right angle; if one more pair of acute angles is equal, the triangles are similar by the AA criterion.
Q5
The height of an equilateral triangle with side $a$ is:
📝 SolutionDropping an altitude bisects the base, forming a right triangle with hypotenuse $a$ and base $\frac{a}{2}$. By Pythagoras: $h = \sqrt{a^2 - \left(\frac{a}{2}\right)^2} = \frac{\sqrt{3}}{2}a$.
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Class 10 · Maths
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