Introduction to Euclid’s Geometry — Maths STD 9 — Question

Study the following statement:
"Two intersecting lines cannot be perpendicular to the same line". Check whether it is an equivalent version to the Euclid’s fifth postulate.
[Hint: Identify the two intersecting lines l and m and the linen in the above statement]

Factorize the following expressions:
64a³ - b³

A forest ranger keeps track of bears in his area. He plotted their location on a graph. The origin represents the ranger's control room’s location. To access and maintain equipment, Road x and Road yhave been laid and paved inside the forest. They pass through the control room. 

One unit on the graph paper represents 1 km. 
1. Ravi planted a red maple tree sapling. The height of the sapling is 0.25 m. The average growth rate of the height of a red maple tree is 0.27 m per year.
The average life of a red maple tree is 80–100 years. Ravi estimated that his tree will grow up to 27 m.
What is the likely reason behind his estimation?
2. Which of the following equations represents the height (h) of the red maple tree after ‘t’ years of planting?

Factorise:
ab(x² + y²) - xy(a² + b²)

Define the following terms:
Obtuse angle.

Write the following in the expanded form:
(a + 2b + c)²

Evaluate:
48³ - 30³ - 18³

Factorise:
16x⁴ + 54x