Visual lens G Strategy (Concept of similarities) | Easy
In a triangle ABC, AB=AC=12 cm and D is a point on side BC such that AD= 8 cm. If AD is extended to point E such that angle ACB = angle AEB , then length in cm of AE is :
1.16
2.18
3.14
4.20
Answer & Explanation
Based on the information in the question triangle ABD ≈ triangle AEB , Thus :
AB/AE = AD/AB ,
12/AE = 8/12 = 2/3
Only option 2 satisfies the condition. Thus option 2 is the answer
Visual G Strategy | Triplets + Area of Triangles | Moderate
A triangle ABC is formed with AB = AC = 50 cm and BC = 80 cm. Then, the length, in cm , of all three altitudes of the triangle ABC is….. …
Solution & Explanation
Give AB = AC = 50 cm , BC = 80 cm
The altitude from A to BC
Half of BC: 80 / 2 = 40 cm
Use Pythagoras’ theorem to find altitude h:
h² + 40² = 50²
h² + 1600 = 2500
h² = 900 , h = 30 cm
Altitude from A to BC = 30 cm
The altitudes from B and C
Area of the triangle using the altitude from A:
Area = (1/2) × 80 × 30 = 1200 cm²
Using area to find the altitude from B:
1200 = (1/2) × 50 × h
h = 1200 / 25 = 48 cm
Altitude from B to AC = 48 cm
Altitude from C to AB = 48 cm
Sum = 30 + 48 + 48 = 126
Answer 126
Visual G Strategy | Cyclic quadrilateral+ Area of trapezium | Moderate
ABCD is a trapezium in which AB is parallel to DC and AD is perpendicular to AB and AB = 3DC. If a circle inscribed in a trapezium touching all the sides has a radius 3cm , then the area in sq cm , of the trapezium is :
1.48
2.36√2
3.54
4.30√3
Solution & Explanation
Given:
Let the trapezium be ABCD.
AB || DC (The parallel sides are the bases).
AD perpendicular to AB (The trapezium is a right-angle trapezium). AB = 3DC. If AB = x , then DC = 3x
The circle inscribed in the trapezium has a radius r = 3cm
Height = 2r = 2 × 3 = 6cm
For cyclic quadrilateral Sum of parallel sides= Sum of non-parallel sides
AB + DC = AD + BC
3x + x = 6 + BC
BC = 4x – 6 —– I
In Triangle AEB with base BE , height CE and hypotenuse BC
BE = DC – AB = 3x – x = 2x , CE = 6cm , BC = 4x – 6
Using Pythagoras:
(2x)² + (6)² = (4x – 6)²
On solving we have x = 4cm
Area of trapezium = ½ * (AB + DC) × AD
= ½ .(4x) .6 = 48cm² , This option 1 is the answer
