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What is the value of a?
(1) The area of an equilateral triangle of side length 3a units is \(9\sqrt{3}\) square units
(2) The area of an isosceles triangle whose sides are of length 4a, 4a and a units is \(3\sqrt{7}\) square units
(1) The area of an equilateral triangle of side length 3a units is \(9\sqrt{3}\) square units
(2) The area of an isosceles triangle whose sides are of length 4a, 4a and a units is \(3\sqrt{7}\) square units
25 Feb 2020, 07:15
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What is the value of a?
(1) The area of an equilateral triangle of side length 3a units is \(9\sqrt{3}\) square units
(2) The area of an isosceles triangle whose sides are of length 4a, 4a and a units is \(3\sqrt{7}\) square units
(1) The area of an equilateral triangle of side length 3a units is \(9\sqrt{3}\) square units
(2) The area of an isosceles triangle whose sides are of length 4a, 4a and a units is \(3\sqrt{7}\) square units
Solution
Step 1: Analyse Question Stem
We need to find the value of \(a\).
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The area of an equilateral triangle of side length \(3a\) units \(9√3\) square units.
- • With this information we will get an equation of one variable a, and we will take the only positive value of a.
- o Indirectly we can infer that we can find the value of a.
- o \(\frac{√3}{4}*(3a)^2= 9√3\)
o \(a^2 = 4\)
- \(a =2,\) we have discarded the case of -2 because the length can never be negative.
Statement 2: The area of an isosceles triangle whose sides are of 4a, 4a and a unit 3√7 square units.
- • We can find, the height of the triangle in terms of a, and we can form an equation in terms of a and after comparing with the given value of the area, we can find the value of a.
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